Problem: Rewrite as a simplified fraction. ${0.63\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 636.6666...\\ 100x &= 63.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 573}$ ${x = \dfrac{573}{900}} $ ${x = \dfrac{191}{300}} $